1. Psych 231: Research Methods in Psychology
Statistics
Psych 231: Research Methods in Psychology

2. Statistics 2 General kinds of Statistics Descriptive statistics
Used to describe, simplify, & organize data sets
Describing distributions of scores
Inferential statistics
Used to test claims about the population, based on data gathered from samples
Takes sampling error into account, are the results above and beyond what you’d expect by random chance
Statistics

3. Describing Distributions
Visual descriptions - A picture of the distribution is usually helpful
Gives a good sense of the properties of the distribution
Many different ways to display distribution
Graphs
Continuous variable:
histogram, line graph
Categorical variable:
pie chart, bar chart
Tables
Frequency distribution table
Table of condition means and standard deviations
Numerical descriptions of distributions
Describing Distributions

4. Be careful using a line graph for categorical variables
People might interpolate: The line implies that there are responses between Smith and Doe, but there are not
A word of caution

5. Describing Distributions
Properties of a distribution
Shape
Symmetric v. asymmetric (skew)
Unimodal v. multimodal
Center
Where most of the data in the distribution are
Mean, Median, Mode
Spread (variability)
How similar/dissimilar are the scores in the distribution?
Standard deviation (variance), Range
Describing Distributions

6. Properties of distributions: Shape
Symmetric
The two sides line up
Asymmetric (skewed)
The two sides do not line up
Properties of distributions: Shape

7. Properties of distributions: Shape
Unimodal (one mode)
Major mode
Minor mode
Multimodal
Bimodal examples
Properties of distributions: Shape

8. Properties of distributions: Center
There are three main measures of center
Purpose: to use a single score to represent the distribution as a whole
Mean (M): the arithmetic average
Add up all of the scores and divide by the total number
Most used measure of center
Median (Mdn): the middle score in terms of location
The score that cuts off the top 50% of the from the bottom 50%
Good for skewed distributions (e.g. net worth)
Mode: the most frequent score
Good for nominal scales (e.g. eye color)
A must for multi-modal distributions
Properties of distributions: Center

9. The Mean The most commonly used measure of center
The arithmetic average
Computing the mean
Divide by the total number in the population
The formula for the population mean is (a parameter):
Add up all of the X’s
The formula for the sample mean is (a statistic):
Divide by the total number in the sample
The Mean

10. Spread (Variability) How similar are the scores? Low variability
The scores are fairly similar
High variability
The scores are fairly dissimilar
mean
mean
Spread (Variability)

11. Spread (Variability) How similar are the scores?
Range: the maximum value - minimum value
Only takes two scores from the distribution into account
Influenced by extreme values (outliers)
Standard deviation (SD): (essentially) the average amount that the scores in the distribution deviate from the mean
Takes all of the scores into account
Also influenced by extreme values (but not as much as the range)
Variance: standard deviation squared
Spread (Variability)

12. The standard deviation is the most popular and most important measure of variability.
The standard deviation measures how far off all of the individuals in the distribution are from a standard, where that standard is the mean of the distribution.
Essentially, the average of the deviations. μ
Standard deviation

13. An Example: Computing the Mean
Our population
2, 4, 6, 8 μ
An Example: Computing the Mean

14. An Example: Computing Standard Deviation (population)
Step 1: To get a measure of the deviation we need to subtract the population mean from every individual in our distribution.
Our population
2, 4, 6, 8 μ -3
X – μ = deviation scores
2 - 5 = -3
An Example: Computing Standard Deviation (population)

15. An Example: Computing Standard Deviation (population)
Step 1: To get a measure of the deviation we need to subtract the population mean from every individual in our distribution.
Our population
2, 4, 6, 8 μ -1
X – μ = deviation scores
2 - 5 = -3
4 - 5 = -1
An Example: Computing Standard Deviation (population)

16. An Example: Computing Standard Deviation (population)
Step 1: To get a measure of the deviation we need to subtract the population mean from every individual in our distribution.
Our population
2, 4, 6, 8 μ 1
X – μ = deviation scores
2 - 5 = -3
6 - 5 = +1
4 - 5 = -1
An Example: Computing Standard Deviation (population)

17. An Example: Computing Standard Deviation (population)
Step 1: To get a measure of the deviation we need to subtract the population mean from every individual in our distribution.
Our population
2, 4, 6, 8 μ 3
X – μ = deviation scores
2 - 5 = -3
6 - 5 = +1
Notice that if you add up all of the deviations they must equal 0.
4 - 5 = -1
8 - 5 = +3
An Example: Computing Standard Deviation (population)

18. An Example: Computing Standard Deviation (population)
Step 2: So what we have to do is get rid of the negative signs. We do this by squaring the deviations and then taking the square root of the sum of the squared deviations (SS).
SS = Σ(X - μ)2
2 - 5 = -3
4 - 5 = -1
6 - 5 = +1
8 - 5 = +3
X – μ = deviation scores
= (-3)2
+ (-1)2
+ (+1)2
+ (+3)2
= = 20
An Example: Computing Standard Deviation (population)

19. An Example: Computing Standard Deviation (population)
Step 3: ComputeVariance (which is simply the average of the squared deviations (SS))
So to get the mean, we need to divide by the number of individuals in the population.
variance = σ2 = SS/N
An Example: Computing Standard Deviation (population)

20. An Example: Computing Standard Deviation (population)
Step 4: Compute Standard Deviation
To get this we need to take the square root of the population variance.
standard deviation = σ =
An Example: Computing Standard Deviation (population)

21. An Example: Computing Standard Deviation (population)
To review:
Step 1: Compute deviation scores
Step 2: Compute the SS
Step 3: Determine the variance
Take the average of the squared deviations
Divide the SS by the N
Step 4: Determine the standard deviation
Take the square root of the variance
An Example: Computing Standard Deviation (population)

22. An Example: Computing Standard Deviation (sample)
To review:
Step 1: Compute deviation scores
Step 2: Compute the SS
Step 3: Determine the variance
Take the average of the squared deviations
Divide the SS by the N-1
Step 4: Determine the standard deviation
Take the square root of the variance
This is done because samples are biased to be less variable than the population. This “correction factor” will increase the sample’s SD (making it a better estimate of the population’s SD)
An Example: Computing Standard Deviation (sample)

23. Statistics Why do we use them? Descriptive statistics
Used to describe, simplify, & organize data sets
Describing distributions of scores
Inferential statistics
Used to test claims about the population, based on data gathered from samples
Takes sampling error into account, are the results above and beyond what you’d expect by random chance
Statistics

24. Inferential Statistics
Purpose: To make claims about populations based on data collected from samples
What’s the big deal?
Example Experiment:
Group A - gets treatment to improve memory
Group B - gets no treatment (control)
After treatment period test both groups for memory
Results:
Group A’s average memory score is 80%
Group B’s is 76%
Is the 4% difference a “real” difference (statistically significant) or is it just sampling error?
Inferential Statistics

25. Testing Hypotheses Step 1: State your hypotheses
Step 2: Set your decision criteria
Step 3: Collect your data from your sample(s)
Step 4: Compute your test statistics
Step 5: Make a decision about your null hypothesis
“Reject H0”
“Fail to reject H0”
Testing Hypotheses

26. Testing Hypotheses Step 1: State your hypotheses
This is the hypothesis that you are testing
Null hypothesis (H0)
Alternative hypothesis(ses)
“There are no differences (effects)”
Generally, “not all groups are equal”
You aren’t out to prove the alternative hypothesis (although it feels like this is what you want to do)
If you reject the null hypothesis, then you’re left with support for the alternative(s) (NOT proof!)
Testing Hypotheses

27. Testing Hypotheses Step 1: State your hypotheses
In our memory example experiment
Null H0: mean of Group A = mean of Group B
Alternative HA: mean of Group A ≠ mean of Group B
(Or more precisely: Group A > Group B)
It seems like our theory is that the treatment should improve memory.
That’s the alternative hypothesis. That’s NOT the one the we’ll test with inferential statistics.
Instead, we test the H0
Testing Hypotheses

28. Testing Hypotheses Step 1: State your hypotheses
Step 2: Set your decision criteria
Your alpha level will be your guide for when to:
“reject the null hypothesis”
“fail to reject the null hypothesis”
This could be correct conclusion or the incorrect conclusion
Two different ways to go wrong
Type I error: saying that there is a difference when there really isn’t one (probability of making this error is “alpha level”)
Type II error: saying that there is not a difference when there really is one
Testing Hypotheses

29. Error types Real world (‘truth’) H0 is correct H0 is wrong
Type I error
Reject H0
Experimenter’s conclusions
Fail to Reject H0
Type II error
Error types

30. Error types: Courtroom analogy
Real world (‘truth’)
Defendant is innocent
Defendant is guilty
Type I error
Find guilty
Jury’s decision
Type II error
Find not guilty
Error types: Courtroom analogy

31. Type I error: concluding that there is an effect (a difference between groups) when there really isn’t.
Sometimes called “significance level”
We try to minimize this (keep it low)
Pick a low level of alpha
Psychology: 0.05 and 0.01 most common
Type II error: concluding that there isn’t an effect, when there really is.
Related to the Statistical Power of a test
How likely are you able to detect a difference if it is there
Error types

32. Testing Hypotheses Step 1: State your hypotheses
Step 2: Set your decision criteria
Step 3: Collect your data from your sample(s)
Step 4: Compute your test statistics
Descriptive statistics (means, standard deviations, etc.)
Inferential statistics (t-tests, ANOVAs, etc.)
Step 5: Make a decision about your null hypothesis
Reject H0 “statistically significant differences”
Fail to reject H0 “not statistically significant differences”
Testing Hypotheses

33. Statistical significance
“Statistically significant differences”
When you “reject your null hypothesis”
Essentially this means that the observed difference is above what you’d expect by chance
“Chance” is determined by estimating how much sampling error there is
Factors affecting “chance”
Sample size
Population variability
Statistical significance

34. (Pop mean - sample mean)
Population mean
Population
Distribution x
Sampling error
(Pop mean - sample mean)
n = 1
Sampling error

35. (Pop mean - sample mean)
Population mean
Population
Distribution
Sample mean x x
Sampling error
(Pop mean - sample mean)
n = 2
Sampling error

36. (Pop mean - sample mean)
Generally, as the sample size increases, the sampling error decreases
Population mean
Population
Distribution
Sample mean x
Sampling error
(Pop mean - sample mean)
n = 10
Sampling error

37. Typically the narrower the population distribution, the narrower the range of possible samples, and the smaller the “chance”
Large population variability
Small population variability
Sampling error

38. Sampling error Population Distribution of sample means
These two factors combine to impact the distribution of sample means.
The distribution of sample means is a distribution of all possible sample means of a particular sample size that can be drawn from the population
Population
Distribution of sample means XC
Samples of size = n XA XD
Avg. Sampling error XB
“chance”
Sampling error

39. Significance “A statistically significant difference” means:
the researcher is concluding that there is a difference above and beyond chance
with the probability of making a type I error at 5% (assuming an alpha level = 0.05)
Note “statistical significance” is not the same thing as theoretical significance.
Only means that there is a statistical difference
Doesn’t mean that it is an important difference
Significance

40. Non-Significance Failing to reject the null hypothesis
Generally, not interested in “accepting the null hypothesis” (remember we can’t prove things only disprove them)
Usually check to see if you made a Type II error (failed to detect a difference that is really there)
Check the statistical power of your test
Sample size is too small
Effects that you’re looking for are really small
Check your controls, maybe too much variability
Non-Significance

41. From last time XA XB About populations Example Experiment:
Group A - gets treatment to improve memory
Group B - gets no treatment (control)
After treatment period test both groups for memory
Results:
Group A’s average memory score is 80%
Group B’s is 76%
H0: μA = μB
H0: there is no difference between Grp A and Grp B
Real world (‘truth’)
H0 is correct
H0 is wrong
Experimenter’s conclusions
Reject H0
Fail to Reject H0
Type I error
Type II error
Is the 4% difference a “real” difference (statistically
significant) or is it just sampling error?
Two sample
distributions XA XB
76%
80%
From last time

42. “Generic” statistical test
Tests the question:
Are there differences between groups due to a treatment?
H0 is true (no treatment effect)
Real world (‘truth’)
H0 is correct
H0 is wrong
Experimenter’s conclusions
Reject H0
Fail to Reject H0
Type I error
Type II error
Two possibilities in the “real world”
One population
Two sample
distributions XA XB
76%
80%
“Generic” statistical test

43. “Generic” statistical test
Tests the question:
Are there differences between groups due to a treatment?
Real world (‘truth’)
H0 is correct
H0 is wrong
Experimenter’s conclusions
Reject H0
Fail to Reject H0
Type I error
Type II error
Two possibilities in the “real world”
H0 is true (no treatment effect)
H0 is false (is a treatment effect)
Two populations XA XB XB XA
76%
80%
76%
80%
People who get the treatment change,
they form a new population
(the “treatment population)
“Generic” statistical test

44. “Generic” statistical testXB XA
ER: Random sampling error
ID: Individual differences (if between subjects factor)
TR: The effect of a treatment
Why might the samples be different?
(What is the source of the variability between groups)?
“Generic” statistical test

45. “Generic” statistical testXB XA
ER: Random sampling error
ID: Individual differences (if between subjects factor)
TR: The effect of a treatment
The generic test statistic - is a ratio of sources of variability
Observed difference
TR + ID + ER
ID + ER
Computed
test statistic = =
Difference from chance
“Generic” statistical test

46. Sampling error Population “chance” Distribution of sample means
The distribution of sample means is a distribution of all possible sample means of a particular sample size that can be drawn from the population
Population
Distribution of sample means XC
Samples of size = n XA XD
Avg. Sampling error XB
“chance”
Sampling error

47. “Generic” statistical test
The generic test statistic distribution
To reject the H0, you want a computed test statistics that is large
reflecting a large Treatment Effect (TR)
What’s large enough? The alpha level gives us the decision criterion
TR + ID + ER
ID + ER
Distribution of the test statistic
Test statistic
Distribution of sample means
-level determines where these boundaries go
“Generic” statistical test

48. “Generic” statistical test
The generic test statistic distribution
To reject the H0, you want a computed test statistics that is large
reflecting a large Treatment Effect (TR)
What’s large enough? The alpha level gives us the decision criterion
Distribution of the test statistic
Reject H0
Fail to reject H0
“Generic” statistical test

49. “Generic” statistical test
The generic test statistic distribution
To reject the H0, you want a computed test statistics that is large
reflecting a large Treatment Effect (TR)
What’s large enough? The alpha level gives us the decision criterion
Distribution of the test statistic
Reject H0
“One tailed test”: sometimes you know to expect a particular difference (e.g., “improve memory performance”)
Fail to reject H0
“Generic” statistical test

50. “Generic” statistical test
Things that affect the computed test statistic
Size of the treatment effect
The bigger the effect, the bigger the computed test statistic
Difference expected by chance (sample error)
Sample size
Variability in the population
“Generic” statistical test

51. Significance “A statistically significant difference” means:
the researcher is concluding that there is a difference above and beyond chance
with the probability of making a type I error at 5% (assuming an alpha level = 0.05)
Note “statistical significance” is not the same thing as theoretical significance.
Only means that there is a statistical difference
Doesn’t mean that it is an important difference
Significance

52. Non-Significance Failing to reject the null hypothesis
Generally, not interested in “accepting the null hypothesis” (remember we can’t prove things only disprove them)
Usually check to see if you made a Type II error (failed to detect a difference that is really there)
Check the statistical power of your test
Sample size is too small
Effects that you’re looking for are really small
Check your controls, maybe too much variability
Non-Significance

53. Some inferential statistical tests
1 factor with two groups
T-tests
Between groups: 2-independent samples
Within groups: Repeated measures samples (matched, related)
1 factor with more than two groups
Analysis of Variance (ANOVA) (either between groups or repeated measures)
Multi-factorial
Factorial ANOVA
Some inferential statistical tests

54. T-test Design Formula: Observed difference X1 - X2 T =
2 separate experimental conditions
Degrees of freedom
Based on the size of the sample and the kind of t-test
Formula:
Observed difference
T =
X X2
Diff by chance
Based on sample error
Computation differs for
between and within t-tests
T-test

55. T-test Reporting your results
The observed difference between conditions
Kind of t-test
Computed T-statistic
Degrees of freedom for the test
The “p-value” of the test
“The mean of the treatment group was 12 points higher than the control group. An independent samples t-test yielded a significant difference, t(24) = 5.67, p < 0.05.”
“The mean score of the post-test was 12 points higher than the pre-test. A repeated measures t-test demonstrated that this difference was significant significant, t(12) = 5.67, p < 0.05.”
T-test

56. Analysis of Variance XB XA XC Designs Test statistic is an F-ratio
More than two groups
1 Factor ANOVA, Factorial ANOVA
Both Within and Between Groups Factors
Test statistic is an F-ratio
Degrees of freedom
Several to keep track of
The number of them depends on the design
Analysis of Variance

57. Analysis of Variance More than two groups F-ratio = XB XA XC
Now we can’t just compute a simple difference score since there are more than one difference
So we use variance instead of simply the difference
Variance is essentially an average difference
Observed variance
Variance from chance
F-ratio =
Analysis of Variance

58. 1 factor ANOVA 1 Factor, with more than two levels XB XA XC
Now we can’t just compute a simple difference score since there are more than one difference
A - B, B - C, & A - C
1 factor ANOVA

59. 1 factor ANOVA The ANOVA tests this one!! XA = XB = XC XA ≠ XB ≠ XC
Null hypothesis:
H0: all the groups are equal
The ANOVA tests this one!!
XA = XB = XC
Do further tests to pick between these
Alternative hypotheses
HA: not all the groups are equal
XA ≠ XB ≠ XC
XA ≠ XB = XC
XA = XB ≠ XC
XA = XC ≠ XB
1 factor ANOVA

60. 1 factor ANOVA Planned contrasts and post-hoc tests:
- Further tests used to rule out the different Alternative hypotheses
XA ≠ XB ≠ XC
Test 1: A ≠ B
XA = XB ≠ XC
Test 2: A ≠ C
XA ≠ XB = XC
Test 3: B = C
XA = XC ≠ XB
1 factor ANOVA

61. 1 factor ANOVA Reporting your results The observed differences
Kind of test
Computed F-ratio
Degrees of freedom for the test
The “p-value” of the test
Any post-hoc or planned comparison results
“The mean score of Group A was 12, Group B was 25, and Group C was 27. A 1-way ANOVA was conducted and the results yielded a significant difference, F(2,25) = 5.67, p < Post hoc tests revealed that the differences between groups A and B and A and C were statistically reliable (respectively t(1) = 5.67, p < 0.05 & t(1) = 6.02, p <0.05). Groups B and C did not differ significantly from one another”
1 factor ANOVA

62. We covered much of this in our experimental design lecture
More than one factor
Factors may be within or between
Overall design may be entirely within, entirely between, or mixed
Many F-ratios may be computed
An F-ratio is computed to test the main effect of each factor
An F-ratio is computed to test each of the potential interactions between the factors
Factorial ANOVAs

63. Factorial ANOVAs Reporting your results The observed differences
Because there may be a lot of these, may present them in a table instead of directly in the text
Kind of design
e.g. “2 x 2 completely between factorial design”
Computed F-ratios
May see separate paragraphs for each factor, and for interactions
Degrees of freedom for the test
Each F-ratio will have its own set of df’s
The “p-value” of the test
May want to just say “all tests were tested with an alpha level of 0.05”
Any post-hoc or planned comparison results
Typically only the theoretically interesting comparisons are presented
Factorial ANOVAs

64. Non-Experimental designs
Sometimes you just can’t perform a fully controlled experiment
Because of the issue of interest
Limited resources (not enough subjects, observations are too costly, etc).
Surveys
Correlational
Quasi-Experiments
Developmental designs
Small-N designs
This does NOT imply that they are bad designs
Just remember the advantages and disadvantages of each
Non-Experimental designs

65. Quasi-experiments What are they? General types
Almost “true” experiments, but with an inherent confounding variable
General types
An event occurs that the experimenter doesn’t manipulate
Something not under the experimenter’s control
(e.g., flashbulb memories for traumatic events)
Interested in subject variables
high vs. low IQ, males vs. females
Time is used as a variable
Quasi-experiments

66. Quasi-experiments Program evaluation
Research on programs that is implemented to achieve some positive effect on a group of individuals.
e.g., does abstinence from sex program work in schools
Steps in program evaluation
Needs assessment - is there a problem?
Program theory assessment - does program address the needs?
Process evaluation - does it reach the target population? Is it being run correctly?
Outcome evaluation - are the intended outcomes being realized?
Efficiency assessment- was it “worth” it? The the benefits worth the costs?
Quasi-experiments

67. Quasi-experiments Nonequivalent control group designs
with pretest and posttest (most common)
(think back to the second control lecture)
participants
Experimental
group
Control
Measure
Non-Random
Assignment
Independent Variable
Dependent Variable
But remember that the results may be compromised because of the nonequivalent control group (review threats to internal validity)
Quasi-experiments

68. Quasi-experiments Advantages Disadvantages
Allows applied research when experiments not possible
Threats to internal validity can be assessed (sometimes)
Disadvantages
Threats to internal validity may exist
Designs are more complex than traditional experiments
Statistical analysis can be difficult
Most statistical analyses assume randomness
Quasi-experiments

69. Non-Experimental designs
Sometimes you just can’t perform a fully controlled experiment
Because of the issue of interest
Limited resources (not enough subjects, observations are too costly, etc).
Surveys
Correlational
Quasi-Experiments
Developmental designs
Small-N designs
This does NOT imply that they are bad designs
Just remember the advantages and disadvantages of each
Non-Experimental designs

70. Developmental designs
Used to study changes in behavior that occur as a function of age changes
Age typically serves as a quasi-independent variable
Three major types
Cross-sectional
Longitudinal
Cohort-sequential
Developmental designs

71. Developmental designs
Cross-sectional design
Groups are pre-defined on the basis of a pre-existing variable
Study groups of individuals of different ages at the same time
Use age to assign participants to group
Age is subject variable treated as a between-subjects variable
Age 4
Age 7
Age 11
Developmental designs

72. Developmental designs
Cross-sectional design
Advantages:
Can gather data about different groups (i.e., ages) at the same time
Participants are not required to commit for an extended period of time
Developmental designs

73. Developmental designs
Cross-sectional design
Disavantages:
Individuals are not followed over time
Cohort (or generation) effect: individuals of different ages may be inherently different due to factors in the environment
Are 5 year old different from 15 year olds just because of age, or can factors present in their environment contribute to the differences?
Imagine a 15yr old saying “back when I was 5 I didn’t have a Wii, my own cell phone, or a netbook”
Does not reveal development of any particular individuals
Cannot infer causality due to lack of control
Developmental designs

74. Developmental designs
Longitudinal design
Follow the same individual or group over time
Age is treated as a within-subjects variable
Rather than comparing groups, the same individuals are compared to themselves at different times
Changes in dependent variable likely to reflect changes due to aging process
Changes in performance are compared on an individual basis and overall
Age 11
time
Age 20
Age 15
Developmental designs

75. Longitudinal Designs Example Wisconsin Longitudinal Study (WLS)
Began in 1957 and is still on-going (50 years)
10,317 men and women who graduated from Wisconsin high schools in 1957
Originally studied plans for college after graduation
Now it can be used as a test of aging and maturation
Longitudinal Designs

76. Developmental designs
Longitudinal design
Advantages:
Can see developmental changes clearly
Can measure differences within individuals
Avoid some cohort effects (participants are all from same generation, so changes are more likely to be due to aging)
Developmental designs

77. Developmental designs
Longitudinal design
Disadvantages
Can be very time-consuming
Can have cross-generational effects:
Conclusions based on members of one generation may not apply to other generations
Numerous threats to internal validity:
Attrition/mortality
History
Practice effects
Improved performance over multiple tests may be due to practice taking the test
Cannot determine causality
Developmental designs

78. Developmental designs
Cohort-sequential design
Measure groups of participants as they age
Example: measure a group of 5 year olds, then the same group 10 years later, as well as another group of 5 year olds
Age is both between and within subjects variable
Combines elements of cross-sectional and longitudinal designs
Addresses some of the concerns raised by other designs
For example, allows to evaluate the contribution of cohort effects
Developmental designs

79. Developmental designs
Cohort-sequential design
Time of measurement
Cross-sectional component
1975
1985
1995
Age 5
Age 15
Age 25
Cohort A
1970s
Age 5
Age 15
Cohort B
1980s
Age 5
Cohort C
1990s
Longitudinal component
Developmental designs

80. Developmental designs
Cohort-sequential design
Advantages:
Get more information
Can track developmental changes to individuals
Can compare different ages at a single time
Can measure generation effect
Less time-consuming than longitudinal (maybe)
Disadvantages:
Still time-consuming
Need lots of groups of participants
Still cannot make causal claims
Developmental designs

81. Small N designs What are they?
Historically, these were the typical kind of design used until 1920’s when there was a shift to using larger sample sizes
Even today, in some sub-areas, using small N designs is common place
(e.g., psychophysics, clinical settings, expertise, etc.)
Small N designs

82. Small N designs One or a few participants
Data are typically not analyzed statistically; rather rely on visual interpretation of the data
Observations begin in the absence of treatment (BASELINE)
Then treatment is implemented and changes in frequency, magnitude, or intensity of behavior are recorded
Small N designs

83. Small N designs Baseline experiments – the basic idea is to show:
when the IV occurs, you get the effect
when the IV doesn’t occur, you don’t get the effect (reversibility)
Before introducing treatment (IV), baseline needs to be stable
Measure level and trend
Small N designs

84. Small N designs Level – how frequent (how intense) is behavior?
Are all the data points high or low?
Trend – does behavior seem to increase (or decrease)
Are data points “flat” or on a slope?
Small N designs

85. ABA design ABA design (baseline, treatment, baseline)
The reversibility is necessary, otherwise
something else may have caused the effect
other than the IV (e.g., history, maturation, etc.)
ABA design

86. Small N designs Advantages
Focus on individual performance, not fooled by group averaging effects
Focus is on big effects (small effects typically can’t be seen without using large groups)
Avoid some ethical problems – e.g., with non-treatments
Allows to look at unusual (and rare) types of subjects (e.g., case studies of amnesics, experts vs. novices)
Often used to supplement large N studies, with more observations on fewer subjects
Small N designs

87. Small N designs Disadvantages
Effects may be small relative to variability of situation so NEED more observation
Some effects are by definition between subjects
Treatment leads to a lasting change, so you don’t get reversals
Difficult to determine how generalizable the effects are
Small N designs

88. Some researchers have argued that Small N designs are the best way to go.
The goal of psychology is to describe behavior of an individual
Looking at data collapsed over groups “looks” in the wrong place
Need to look at the data at the level of the individual
Small N designs